Math 1 · Lesson 6 · part 6 of 6
Practice Problems
Try them, get help one step at a time, then print how it went.
Warm-up: read, test, flip
Four short ones before the real solving. Say the property out loud as you type.
Practice: try it, then get help one step at a time
Try each problem yourself first. Hint gives a nudge, Show next step shows one worked step at a time, Reveal answer checks, and Hide help / start over clears the card. Every problem asks two things: did the sign flip, and what is the solution. The problems climb from one move to a full solution you name line by line.
My results
Finished the practice? Print a page that shows each question, what you typed or chose, the correct answer, and how it went. Good for showing a teacher or keeping in a folder.
Exit ticket
On paper or an index card. Use the math word and the plain-English word.
- Read −4 > −9 out loud. Which number is the gator eating, and why is that the right one?
- Solve 2 - 3x ≤ 11. Show Step 1, name the property on every line, say where the sign flips, and check three numbers.
- Solve 5x + 1 > 2x + 10. Which x term did you move, and did you need to flip?
- A friend solved −2x < 8 and wrote x < −4. Use one test number to show the friend it is wrong, then write the right answer.
Check your exit ticket
- Negative four is greater than negative nine. The gator eats the −4, because −4 is to the right of −9 on the number line, so it is the bigger number. Being closer to zero on the negative side means bigger.
- Step 1: 2 + (−3)x ≤ 11 (subtracting 3x is adding its additive inverse, the opposite). Add −2 to both sides by the addition property of inequality (add the same thing to both sides, and the sign stays the same): (−3)x ≤ 9. Multiply both sides by −13, the multiplicative inverse (the reciprocal) of −3. That is the multiplication property of inequality for a negative number, so this is where the sign flips: x ≥ −3. Check: x = 0 gives 2 ≤ 11, true. x = −3, the boundary, gives 2 + 9 = 11 ≤ 11, true, so it is included. x = −4 gives 2 + 12 = 14 ≤ 11, false.
- Step 1: 5x + 1 > 2x + 10 has nothing to rewrite. The coefficients (the numbers on the variables) are 5 and 2, so move the 2x: add −2x to both sides, giving 3x + 1 > 10 by the distributive property run backwards (factoring, pulling out what the terms share). Add −1 to both sides: 3x > 9. Multiply both sides by 13, positive, no flip: x > 3. No flip was needed because the x term we kept has a positive coefficient (the number on the variable).
- Test x = 0 in the original: −2 × 0 = 0, and 0 < 8 is true, so 0 must be a solution. But 0 < −4 is false, so the friend's answer leaves out a number that works. The friend multiplied both sides by −12, a negative number, and forgot to flip. The right answer is x > −4, and 0 > −4 is true.